A store is about to order deluxe, standard and economy grade DVD players for next years inventory. The state of nations economy (fate) during the year will be a factor on sales for that year. Records over the past 5 yrs show if the economy is up, the store will net 4,2, and 1 million dollars, respectively, on sales of deluxe, standard and economy is down, the company will net -1,2, and 4 million dollars, respectively, on sales of deluxe, standard and economy grade models.

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# 1 Answer

With questions like this, there is usually a probably associated with each stage of the economy, such as a
**25% chance of the economy being "down."** This would then entail there's a
**75% change of the economy being "up."** Since there are no probabilities associated with this question, it's impossible to completely answer. We can use a the example probabilities above to illustrate the process needed to complete this question.

From here, we then use an expected value equation: E(x) = P(x_{1}) * X_{1} + P(x_{2}) * X_{2} + .... P(x_{n}) + X_{n}_{
}

This would continue on to X, X4, etc. to the exact number of stages or categories we have within the problem. Since there are only two stages and two type of DVD players in this problem, there will be 2 sections to multiply then add.

**E(DVD Sales) = P(up)*(Up Deluxe Sales + Up Standard Sales) + P(down)*(Down Deluxe Sales + Down Standard Sales)**

= 0.75*($4.2M + $1M) + 0.25*(-$1.2M + $4M)

= 0.75*($5.2) + 0.25*($2.8M)

** answer* = $3.9M + $0.7M = $4.6M**

* This value will change depending on which probability values you use for each stage of the economy. In this particular setup, the company made $4.2M in sales. Play around with different probabilities (%'s) of each stage to see how the expected value changes. Just remember that the probabilities of all the stage must add up to 100% or 1. (75% + 25% = 100%).